Joint Models: Implementation in INLA and Applications

Longitudinal data is encountered when repeated measurements are performed on subjects over aperiod of time. Many models exist to fit longitudinal data, all sharing the feature that explanatorycovariates are introduced into the model to explain the observed change over time. A special type ofcovariate found within the longitudinal framework is the time-varying covariate, such as the BMI orblood biomarker levels. These covariates, whose value changes over time, are a blessing in disguise.On one hand they allow the researcher to better model the change in outcome over time, and thus fita better model. On the other hand bias can be introduced when the time-varying covariates dependon the outcome or its previous values.Time-varying covariates that introduce such bias are called endogenous time-varying covariates:these are covariates whose current value, given their own history, depends on past values of theoutcome. In the presence of such endogenous covariates, because of the cross...Show moreLongitudinal data is encountered when repeated measurements are performed on subjects over aperiod of time. Many models exist to fit longitudinal data, all sharing the feature that explanatorycovariates are introduced into the model to explain the observed change over time. A special type ofcovariate found within the longitudinal framework is the time-varying covariate, such as the BMI orblood biomarker levels. These covariates, whose value changes over time, are a blessing in disguise.On one hand they allow the researcher to better model the change in outcome over time, and thus fita better model. On the other hand bias can be introduced when the time-varying covariates dependon the outcome or its previous values.Time-varying covariates that introduce such bias are called endogenous time-varying covariates:these are covariates whose current value, given their own history, depends on past values of theoutcome. In the presence of such endogenous covariates, because of the cross-reliance of the endoge-nous covariate on the outcome, standard Mixed Models are no longer valid and one needs to resortto joint modelling of both the outcome and the endogenous covariate.In this thesis several such joint longitudinal models will be discussed. Our focus will be on JointMixed Models and Joint Scaled Models. Both explicitly model the dependence between the outcomeand the endogenous covariate, thereby removing the possible bias incurred by the time-varying co-variate. We shall show how to fit these models using a novel Bayesian technique called INLA (In-tegrated Nested Laplace Integration), which is an elegant technique and a good alternative for thecomplex and long MCMC estimation procedure. Although INLA has seen rapid development overrecent years, joint longitudinal models have so far received little attention. The goal of this thesisis therefore to implement several joint longitudinal models within the INLA framework and applythem on a simulation study as well as on a synthetic version of a clinical dataset.Show less

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Joint Models: Implementation in INLA and Applications